Bring large pot of salted water to boil. Cook spaghetti to al dente and drain completely. Replace pot to medium heat.
Melt butter and cook garlic 1 minute until fragrant. Stir in evaporated milk, lemon, salt and pepper. Cook another 2 minutes, simmering gently.
Reduce heat to low and toss with spaghetti, basil and cheese. Continue tossing until sauce starts sticking to pasta and becoming thicker, about 5 minutes. Taste, adjust salt and pepper and serve immediately.